Interestingly, I was in the circuit at Cambridge 10 days ago when ATC had a grumble at a joiner who joined crosswind from the deadside when asked to join overhead. It's clear that Cambridge ATC (for whom I have a great deal of respect) thinks there's a difference, but I have a lot of sympathy with those who aren't on the same page.
In case I wasn't clear, that's what I meant. This was quite a few years ago when I assumed that if asked to do an OHJ from the dead side, it was OK to descend straight away. They were grumbling only because they said OHJ and I wasn't doing it properly.
Personally, I think there's very limited value in an overhead join at a controlled airfield.
I agree. But I do what I'm told by ATC unless there's a pretty good reason not to!